British tourist detained by US authorities for 10 days over visa issue

Probably shouldn't tell border patrol you're doing unpaid labor in a country you're visiting. When speaking to authorities it's best to say the absolute minimum required for the encounter.

I've never had anything to do with foreign exchange students, but are they absolutely prohibited from work of any kind?

If there is ambiguity, then we can't have them here.

In the US, it's very clear. If they don't have work authorization from USCIS, they shouldn't be doing work. There's some guidelines out there on the internet [1], but the students should be extremely careful; any form of compensation or expectation of future compensation for their work could put them in serious trouble. The University of Michigan has a more fleshed out guideline page for their international students [2].

[1] https://marksgray.com/immigration-blog/can-foreign-nationals...

[2] https://internationalcenter.umich.edu/students/employment-vo...

Musk is lucky enforcement wasn't as strict back then.

Cannot citizenship be revoked for past violations?